Related papers: General Quartic $\beta$-Function at Three Loops
A number of DR-bar renormalization constants in softly broken SUSY-QCD are evaluated to three-loop level: the wave function renormalization constants for quarks, squarks, gluons, gluinos, ghosts, and epsilon-scalars, and the renormalization…
We present the results for three-loop gauge field anomalous dimensions in the SM calculated in the background field gauge within the unbroken phase of the model. The results are valid for the general background field gauge parameterized by…
In the case of using the higher derivative regularization for $N=1$ SQED with $N_f$ flavors the loop integrals giving the $\beta$-function are integrals of double total derivatives in the momentum space. This feature allows to reduce one of…
Recently, evidence was provided for the existence of an $a$-function for renormalisable quantum field theories in three dimensions. An explicit expression was given at lowest order for general theories involving scalars and fermions, and…
We consider the Resonance Chiral Theory with one multiplet of scalar and pseudoscalar resonances, up to bilinear couplings in the resonance fields, and evaluate its beta-function at one-loop with the use of the background field method. Thus…
We compute the beta-function and the anomalous dimension of all the non-derivative operators of the theory up to three-loops for the most general nearest-neighbour O(N)-invariant action together with some contributions to the four-loop…
We find the three-loop contribution to the $\beta$-function of ${\cal N}=1$ supersymmetric gauge theories regularized by higher covariant derivatives produced by the supergraphs containing loops of the Faddeev--Popov ghosts. This is done…
For arbitrary four-dimensional quantum field theories with scalars and fermions, renormalisation group equations in the $\overline{\text{MS}}$ scheme are investigated at three-loop order in perturbation theory. Collecting literature…
We deduce the gluino contribution to the three-loop QCD \beta function within the minimal supersymmetric Standard Model (MSSM) from its standard QCD expression. The result is a first step in the computation of the full MSSM three-loop \beta…
We evaluate the one-loop $\beta$ functions of all dimension 6 parity-preserving operators in the Abelian Higgs-Kibble model. No on-shell restrictions are imposed; and the (generalized) non-polynomial field redefinitions arising at one-loop…
The integrals defining the two-loop beta-function for the general renormalizable N=1 supersymmetric Yang--Mills theory, regularized by higher covariant derivatives, are investigated. It is shown that they are given by integrals of double…
Generalisations of the bent property of a boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic boolean functions are related to simple graphs and it is shown…
We give a parameterized generalization of the sum formula for quadruple zeta values. The generalization has four parameters, and is invariant under a cyclic group of order four. By substituting special values for the parameters, we also…
Effective field theories provide a suitable framework for both particle physics and statistical physics. We delve deeper into the study of the effective three-dimensional scalar field theory for its application to statistical physics,…
We complete the two-loop calculation of beta-functions for vacuum expectation values (VEVs) in gauge theories by the missing O(g^4)-terms. The full two-loop results are presented for generic and supersymmetric theories up to two-loop level…
We compute the beta functions of the three Standard Model gauge couplings to four-loop order in the modified minimal subtraction scheme. At this order a proper definition of $\gamma_5$ in $D=4-2\epsilon$ space-time dimensions is required;…
The paper studies the quantum action for the five-dimensional real $\phi^3$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization…
The four-loop beta-function of quantum chromodynamics is calculated and agreement is found with the previous result. The anomalous dimensions of the quark-gluon vertex, and quark, gluon and ghost fields are given for a general compact…
We calculate the third coefficient of the lattice $\beta$ function in pure Yang-Mills theory. We make use of a computer code for solving perturbation theory analytically on the lattice. We compute the divergent integrals by using a method…
Some calculations in supersymmetric theories, made with the higher derivative regularization, show that the beta-function is given by integrals of total derivatives. This is qualitatively explained for the N=1 supersymmetric electrodynamics…